x^y < y^x <=> x^{1/x} < y^{1/y}, so a sufficient condition is that x^{1/x} is decreasing, which is equivalent to f(x) = ln(x)/x being decreasing.
f'(x) = (1-ln(x))/x^2, so it suffices to have x > e.
f'(x) = (1-ln(x))/x^2, so it suffices to have x > e.
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